Word Problems (algebra)

This is more Q&A on how to solve don't bother solving it.

1. Write an equation that can be used to solve the problem. The answer the question asked. A group of college students are volunteering for habitat for humanity during their spring break. They are putting the finishing touches on a house they built. Working alone, Kathy can paint a certain room in 4 hours. Rhonda can paint the same room in 6 hours. How long will it take them working together to paint the room?

In this problem what would X be? The amount of rooms? Which in this case would be 1?

2. The sum of the reciprocal of a number and the reciprocal of 6 less than the number is 8 times the reciprocal of the original number. Find the original number.

Should I set up some sort of formula or should I just do guess and check and follow what it says until I guess the original number?